Particle interference

Today my lecturer talked a little about quasiparticle interference (QPI). He said that if we place a QP on a metal containing a single impurity, then the QP wavepacket will travel outwards, and when it hits the impurity, it will get reflected back and create standing waves.

I don't understand why there are being created standing waves? I mean, we have a wavepacket expanding out from a point, and then it hits the impurity. Then some of the wave is reflected back: Then what is left for the back-reflected wave to interfere with?